Scattering off of a resonant barrier

Here is a little Java applet for investigating the phase-shifts for
s-wave scattering off of a square well. The applet makes use of an
engine called
LiveGraphics3D .

Move your mouse over the square below, and the applet should load.

On
the left is the potential. By dragging the nine black points you can
change the potential. The scattering length is given by a red and
dot. Units are chosen so that hbar=m=1. On the right is the scattering
phase shift as a function of k.

Some points to note: 1) When a bound state is just below threshold,
the scattering length is large and positive. 2) When the resonant state
is just above threshold, the scattering length is large and negative.
3) The phase shift at k=0 gives the number of bound states. 4) The
phase shift vanishes at k=infinity. 5) A finite energy resonance
leads to a jump of pi of the phase shift. 6) The jump becomes
sharper if the barrier is made taller or thicker.